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Compton Scattering - Energy Conservation

  1. Oct 22, 2009 #1
    1. The problem statement, all variables and given/known data

    Using conservation of relativistic energy and momentum, show that for Compton scattering from a free electron, the energy-angle formula for the electron is

    [tex]T=m_0c^2\frac{2\alpha^2cos^2\phi}{1+2\alpha+\alpha^2sin^2\phi}[/tex]

    where

    T = kinetic energy given to electon
    [tex]\phi[/tex] = electron recoil angle
    [tex]\alpha=\frac{h\nu}{m_0c^2}[/tex]
    [tex]h\nu[/tex] = incident photon energy
    [tex]m_0c^2[/tex] = electron rest energy


    2. Relevant equations
    [tex]T=h\nu-h\nu'[/tex]
    [tex]h\nu+m_0c^2=h\nu'+\sqrt{(m_0c^2)^2+(cp_e)^2}[/tex]
    [tex]p_e^2=p_\gamma^2+p_{\gamma'}^2-2p_\gamma p_{\gamma'}}cos\phi[/tex]


    3. The attempt at a solution
    I did a problem similar to this in which I proved that the photoelectric effect is impossible for a free electron. I've tried taking the expression for p and putting it into the energy conservation equation, but what is really baffling me is where is that sin^2 term coming from?? If someone can tell me where it comes in I will probably be well on my way to solving this problem... Thanks!
     
  2. jcsd
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